The present invention relates to a new and distinct Penstemon plant given the name ‘TNPENHM’. Penstemon is in the family Scrophulariaceae. Penstemon ‘TNPENHM’ originated from open-pollinated seeds of Penstemon ‘165-3’, an unnamed, unpatented, proprietary plant. It was part of a controlled breeding program to create a compact, upright, medium- to small-size, reblooming, and hardy series. This seedling was selected for its medium-size red-pink flowers with white throats; flowers in dense clusters; long bloom time; good rebloom; compact, upright, well-branched habit with multiple crowns from the base; vigor; and clean, attractive look. It is an ideal plant for a sunny border in full sun.